Well I think a recent paper about the Hayonim burials with dogs which are about eleven and a half 12,000 years old suggests that you get the earliest dogs in that part of the world with the Natufian culture.

Seventy-two of the skeletons fall into the Natufian period, which predates settled agriculture.

Extensive remains have been found of the Natufian hunter-gatherers, who lived between about 12,800 and 10,500 years ago in what are now Israel, the West Bank, Jordan, Lebanon, and Syria.